Abstract
Heterotic backgrounds with torsion preserving minimal supersymmetry in four dimensions can be obtained as orbifolds of principal T2 bundles over K3. We consider a worldsheet description of these backgrounds as gauged linear sigma-models (GLSMs) with (0, 2) supersymmetry. Such a formulation provides a useful framework in order to address the resolution of singularities of the orbifold geometries. We investigate the constraints imposed by discrete symmetries on the corresponding torsional GLSMs. In particular, the principal T2 connection over K3 is inherited from (0, 2) vector multiplets. As these vectors gauge global scaling symmetries of products of projective spaces, the corresponding K3 geometry is naturally realized as an algebraic hypersurface in such a product (or as a branched cover of it). We outline the general construction for describing such orbifolds. We give explicit constructions for automorphisms of order two and three.
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References
S.-T. Yau, On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I, Commun. Pure Appl. Math. 31 (1978) 339 [INSPIRE].
S.K. Donaldson, Anti Self-Dual Yang-Mills Connections over Complex Algebraic Surfaces and Stable Vector Bundles, Proc. Lond. Math. Soc. 50 (1985) 1 [INSPIRE].
K. Uhlenbeck and S.T. Yau, On the existence of hermitian-yang-mills connections in stable vector bundles, Commun. Pure Appl. Math. 39 (1986) S257.
E. Witten, New Issues in Manifolds of SU(3) Holonomy, Nucl. Phys. B 268 (1986) 79 [INSPIRE].
L. Witten and E. Witten, Large Radius Expansion of Superstring Compactifications, Nucl. Phys. B 281 (1987) 109 [INSPIRE].
C.M. Hull, Compactifications of the Heterotic Superstring, Phys. Lett. B 178 (1986) 357 [INSPIRE].
A. Strominger, Superstrings with Torsion, Nucl. Phys. B 274 (1986) 253 [INSPIRE].
K. Dasgupta, G. Rajesh and S. Sethi, M theory, orientifolds and G-flux, JHEP 08 (1999) 023 [hep-th/9908088] [INSPIRE].
M. Becker, L.-S. Tseng and S.-T. Yau, Heterotic Kähler/non-Kähler Transitions, Adv. Theor. Math. Phys. 12 (2008) 1147 [arXiv:0706.4290] [INSPIRE].
T. Banks and L.J. Dixon, Constraints on String Vacua with Space-Time Supersymmetry, Nucl. Phys. B 307 (1988) 93 [INSPIRE].
I.V. Melnikov and R. Minasian, Heterotic Sigma Models with N = 2 Space-Time Supersymmetry, JHEP 09 (2011) 065 [arXiv:1010.5365] [INSPIRE].
M. Becker, L.-S. Tseng and S.-T. Yau, New Heterotic Non-Kähler Geometries, Adv. Theor. Math. Phys. 13 (2009) 1815 [arXiv:0807.0827] [INSPIRE].
C. Borcea, K3 surfaces with involution and mirror pairs of calabi-yau manifolds, in Mirror symmetry II, American Mathematical Society (1996), pp. 717–743 [https://doi.org/10.1090/amsip/001/28].
C. Voisin, Miroirs et involutions sur les surfaces K3, in Journées de géométrie algébrique d’Orsay — Juillet 1992, Astérisque 218, Société mathématique de France (1993) [http://www.numdam.org/item/AST_19___93218___273_0/].
E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].
A. Adams, M. Ernebjerg and J.M. Lapan, Linear models for flux vacua, Adv. Theor. Math. Phys. 12 (2008) 817 [hep-th/0611084] [INSPIRE].
A. Adams and J.M. Lapan, Computing the Spectrum of a Heterotic Flux Vacuum, JHEP 03 (2011) 045 [arXiv:0908.4294] [INSPIRE].
D. Israël, T-Duality in Gauged Linear Sigma-Models with Torsion, JHEP 11 (2013) 093 [arXiv:1306.6609] [INSPIRE].
D. Israël and M. Sarkis, New supersymmetric index of heterotic compactifications with torsion, JHEP 12 (2015) 069 [arXiv:1509.05704] [INSPIRE].
D. Israël and M. Sarkis, Dressed elliptic genus of heterotic compactifications with torsion and general bundles, JHEP 08 (2016) 176 [arXiv:1606.08982] [INSPIRE].
C. Angelantonj, D. Israël and M. Sarkis, Threshold corrections in heterotic flux compactifications, JHEP 08 (2017) 032 [arXiv:1611.09442] [INSPIRE].
S. Groot Nibbelink, Heterotic orbifold resolutions as (2, 0) gauged linear sigma models, Fortsch. Phys. 59 (2011) 454 [arXiv:1012.3350] [INSPIRE].
M. Blaszczyk, S. Groot Nibbelink and F. Ruehle, Gauged Linear Sigma Models for toroidal orbifold resolutions, JHEP 05 (2012) 053 [arXiv:1111.5852] [INSPIRE].
S. Ivanov, Heterotic supersymmetry, anomaly cancellation and equations of motion, Phys. Lett. B 685 (2010) 190 [arXiv:0908.2927] [INSPIRE].
P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum configurations for superstrings, Nucl. Phys. B 258 (1985) 46 [INSPIRE].
E. Goldstein and S. Prokushkin, Geometric model for complex nonKähler manifolds with SU(3) structure, Commun. Math. Phys. 251 (2004) 65 [hep-th/0212307] [INSPIRE].
I.V. Melnikov, R. Minasian and S. Theisen, Heterotic flux backgrounds and their IIA duals, JHEP 07 (2014) 023 [arXiv:1206.1417] [INSPIRE].
I.V. Melnikov, R. Minasian and S. Sethi, Heterotic fluxes and supersymmetry, JHEP 06 (2014) 174 [arXiv:1403.4298] [INSPIRE].
J.-X. Fu and S.-T. Yau, The Theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère equation, J. Diff. Geom. 78 (2008) 369 [hep-th/0604063] [INSPIRE].
K. Becker et al., Anomaly cancellation and smooth non-Kähler solutions in heterotic string theory, Nucl. Phys. B 751 (2006) 108 [hep-th/0604137] [INSPIRE].
J. Distler, Notes on (0, 2) superconformal field theories, hep-th/9502012 [INSPIRE].
V.V. Nikulin, Finite Automorphism Groups of Kähler K3 Surfaces, Trans. Moscow Math. Soc. 38 (1980) 71.
M. Artebani, A. Sarti and S. Taki, K3 surfaces with non-symplectic automorphisms of prime order, Math. Z. 268 (2010) 507.
M. Artebani and A. Sarti, Non-symplectic automorphisms of order 3 on K3 surfaces, Math. Ann. 342 (2008) 903.
S. Chaudhuri, G. Hockney and J.D. Lykken, Maximally supersymmetric string theories in D < 10, Phys. Rev. Lett. 75 (1995) 2264 [hep-th/9505054] [INSPIRE].
S. Kachru and C. Vafa, Exact results for N = 2 compactifications of heterotic strings, Nucl. Phys. B 450 (1995) 69 [hep-th/9505105] [INSPIRE].
S. Ferrara, J.A. Harvey, A. Strominger and C. Vafa, Second quantized mirror symmetry, Phys. Lett. B 361 (1995) 59 [hep-th/9505162] [INSPIRE].
C.M. Hull and P.K. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [INSPIRE].
C. Vafa and E. Witten, Dual string pairs with N = 1 and N = 2 supersymmetry in four-dimensions, Nucl. Phys. B Proc. Suppl. 46 (1996) 225 [hep-th/9507050] [INSPIRE].
V. Braun, On Free Quotients of Complete Intersection Calabi-Yau Manifolds, JHEP 04 (2011) 005 [arXiv:1003.3235] [INSPIRE].
P. Candelas, A.M. Dale, C.A. Lutken and R. Schimmrigk, Complete Intersection Calabi-Yau Manifolds, Nucl. Phys. B 298 (1988) 493 [INSPIRE].
L.B. Anderson, X. Gao, J. Gray and S.-J. Lee, Fibrations in CICY Threefolds, JHEP 10 (2017) 077 [arXiv:1708.07907] [INSPIRE].
J. Gray and J. Wang, Free quotients of favorable Calabi-Yau manifolds, JHEP 07 (2022) 116 [arXiv:2112.12683] [INSPIRE].
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We would like to thank Alessandra Sarti for useful correspondence, and Ruben Minasian for discussions.
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Israël, D., Proto, Y. A worldsheet approach to 𝒩 = 1 heterotic flux backgrounds. J. High Energ. Phys. 2023, 175 (2023). https://doi.org/10.1007/JHEP06(2023)175
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DOI: https://doi.org/10.1007/JHEP06(2023)175